TY - JOUR
T1 - On local and global rigidity of quasi-conformal anosov diffeomorphisms
AU - Kalinin, Boris
AU - Sadovskaya, Victoria
PY - 2003/10
Y1 - 2003/10
N2 - We consider a transitive uniformly quasi-conformal Anosov diffeomorphism [formula omitted] of a compact manifold [formula omitted]. We prove that if the stable and unstable distributions have dimensions greater than two, then [formula omitted] is [formula omitted] conjugate to an affine Anosov automorphism of a finite factor of a torus. If the dimensions are at least two, the same conclusion holds under the additional assumption that [formula omitted] is an infranilmanifold. We also describe necessary and sufficient conditions for smoothness of conjugacy between such a diffeomorphism and a small perturbation. AMS 2000 Mathematics subject classification: Primary 37C; 37D.
AB - We consider a transitive uniformly quasi-conformal Anosov diffeomorphism [formula omitted] of a compact manifold [formula omitted]. We prove that if the stable and unstable distributions have dimensions greater than two, then [formula omitted] is [formula omitted] conjugate to an affine Anosov automorphism of a finite factor of a torus. If the dimensions are at least two, the same conclusion holds under the additional assumption that [formula omitted] is an infranilmanifold. We also describe necessary and sufficient conditions for smoothness of conjugacy between such a diffeomorphism and a small perturbation. AMS 2000 Mathematics subject classification: Primary 37C; 37D.
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U2 - 10.1017/S1474748003000161
DO - 10.1017/S1474748003000161
M3 - Article
AN - SCOPUS:85012565392
SN - 1474-7480
VL - 2
SP - 567
EP - 582
JO - Journal of the Institute of Mathematics of Jussieu
JF - Journal of the Institute of Mathematics of Jussieu
IS - 4
ER -